The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 metres respectively, and the angle contained by the first two sides is a right angle. Find its area.
Let consider a quadrilateral ABCD
In ∆ABC;
AC = 
= 13 m
AB = a = 5 m, BC = b = 12 m, AC = c = 13 m
Let a, b and c are the sides of triangle and s is
the semi-perimeter, then its area is given by:
A = 
where 
[Heron’s Formula]
= 
= 15
A1 = 
A1 = 
= 
m2
In ∆ADC;
DA = a = 15 m, CD = b = 14 m, AC = c = 13 m
Let a, b and c are the sides of triangle and s is
the semi-perimeter, then its area is given by:
A = 
where 
= 
= 21
A2 = 
A2 = 
= 
m2
Therefore area of quadrilateral ABCD = A1 + A2 = 30+84 = 114 m2
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